Problem: Solve for $x$ : $4x^2 - 48x + 144 = 0$
Dividing both sides by $4$ gives: $ x^2 {-12}x + {36} = 0 $ The coefficient on the $x$ term is $-12$ and the constant term is $36$ , so we need to find two numbers that add up to $-12$ and multiply to $36$ The number $-6$ used twice satisfies both conditions: $ {-6} + {-6} = {-12} $ $ {-6} \times {-6} = {36} $ So $(x - {6})^2 = 0$ $x - 6 = 0$ Thus, $x = 6$ is the solution.